Ocular dominance, sometimes called eye dominance or eyedness, is the
tendency to prefer visual input from one eye to the other. It is
somewhat analogous to the laterality of right or left handedness,
however the side of the dominant eye and the dominant hand do not
always match. Approximately two-thirds of the population is
right-eye dominant; however, neither eye is dominant in a small portion
of the population. Dominance does appear to change
depending upon direction of gaze due to image size changes on the
retinas.

There are 3 descriptions of dominance, and it is possible that the dominace for a
person may shift between left- and right eye depending on the type of focus (see topic: 0.4 Shifting Dominance).

1. Directional dominance: sometimes referred to as sighting dominance, is the most
familiar since most of the clinical procedures test for this category
of dominance.

The eye with which one sights.

The eye with which one notices less jump in an alternate cover test.

The directional dominant eye is
determined by subjective alignment of two objects presented at a
stereodisparity far beyond Panum's area, there are a number tests (Wikipedia) one of them is:

The Miles Test:
The observer extends both arms, brings both hands together to create a
small opening, then with both eyes open views a distant object through
the opening. The observer then alternates closing the eyes or slowly
draws opening back to the head to determine which eye is viewing the
object (i.e. the dominant eye).

2. Sensory dominance: It may occur when there is a difference in the two
retinal images that might lead to rivalry or some binocular
interaction. For example, there may be differences in image clarity,
brightness or color. Based on these differences, the visual system
might find it easier to suppress one eye than the other, or to favor
one eye over the other.

The eye whose image is seen more frequently in binocular rivalry.

The eye that has the âmore substantial-seeming imageâ in physiological diplopia.

The eye whose image is less readily ignored, as in monocular microscopy.

3. Oculomotor dominance: It usually refers to the eye that does a better job
of fixating on an object of regard under binocular conditions. For
example, if in a case of fixation disparity, most of the deviation were
in one eye, the other eye would be considered the dominant eye.

The eye that centrally fixates in the presence of a fixation disparity.

Importance of ocular dominance : In normal
binocular vision there is an effect of parallax, and therefore the
dominant eye is the one that is primarily relied on for precise
positional information.

Parallax, or more accurately motion parallax (Greek: alteration)
is the change of angular position of two stationary points relative to
each other as seen by an observer, due to the motion of an observer.
Simply put, it is the apparent shift of an object against a background
due to a change in observer position. It is often thought of as the
'apparent motion' of an object against a distant background (see image) because of a perspective shift. When viewed from A, the object
appears to be closer to the blue square. When the viewpoint is changed
to B, the object appears to have moved in front of the red square.